Points, lines, planes and angles

The most fundamental idea in the study of geometry is the idea of a point. Think of a point as an exact location in space, it has no dimensions. When writing about points, you represent the points by dots. Remember, the dot is only a picture of a point, and not the point itself. Points are commonly refered to by using capital letters. The dots mark points and are refered to as point A, point B and point C.

A line is one of the undefined terms in geometry. A description of a line is that it has length but no thickness or depth. In theory, a line may be extended infinitely in each direction.

A plane is a flat surface that extends infinitely in all directions. Imagine extending the length and width of a table top forever.

Lines that lie in the same plane are called coplanar lines. Any two coplanar lines must have one and only one of the characteristics listed below.

· The lines may intersect. If they intersect and

form right angles, they are perpendicular lines.

· The lines may be parallel. Parallel lines will

never meet.

· The lines may coincide. Lines that coincide are actually the same lines.

Lines that lie in different planes and do not intersect

are called noncoplanar lines or skew lines.

· If two planes do not intersect, the planes are parallel.

· If two planes intersect, their intersection is a line.

An angle is formed by two rays that have the same endpoint, which is called the vertex of the angle. The rays are called the sides of the angle. (A ray is a part of a line drawn from a given point called the endpoint. The ray continues forever in the other direction.) A point between the sides of the angle is in the interior of the angle. " " is the symbol for angle. To name an angle use three letters. The center letter corresponds to the vertex. The other two letters are points on each ray.

The angle can be named ABC or CBA. It can be read as “angle ABC or angle CBA.

An angle is measured in degrees with an instrument called a protractor.

There are five types of angles that are essential to the study of geometry.

Acute angle – an angle whose measure is less than 90°.

Right angle – an angle whose measure equals 90°. A box in the vertex denotes a right angle.

Obtuse angle – an angle whose measure is greater than 90° and less than 180°.

Straight angle – an angle whose measure equals 180°.

Reflex angle – an angle whose measure is greater than 180⁰ and less than 360⁰

· Equal angles are angles that have the same number of degrees.

· A ray that bisects an angle divides it into 2 equal parts. The line is called the angle bisector.

· Congruent angles have the same measure.

· Perpendiculars are lines that form right angles.

· All right angles are congruent.

· The sides of a straight angle lie on a straight line.

· All straight angles are congruent.

· A perpendicular bisector of a line bisects the line and is perpendicular to the line.